{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 13: Rendezvous & CW Equation Tracking\n", "\n", "This tutorial covers **Relative Orbital Mechanics** and relative targeting using the Clohessy-Wiltshire (CW) equations and absolute targeting via Lambert's problem.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Theory Prerequisite\n", "\n", "### 1.1 Clohessy-Wiltshire (Hill's) Equations\n", "Describes the relative motion of a **Chaser** spacecraft with respect to a **Target** spacecraft in a circular orbit.\n", "\n", "- **Frame**: Local-Vertical Local-Horizontal (LVLH)\n", " - $x$: Radial (Away from center)\n", " - $y$: Along-track (Velocity direction)\n", " - $z$: Cross-track (Angular momentum)\n", "\n", "State yields analytical equations of motion when relative distance is $r \\ll r_{target}$.\n", "\n", "### 1.2 Lambert's Problem\n", "Given initial position $r_1$, final position $r_2$, and a time-of-flight $\\Delta t$, determine the initial velocity $v_1$ and final velocity $v_2$ required to connect the two points under Keplerian dynamics." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Imports successful.\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from opengnc.guidance.rendezvous import cw_equations, cw_targeting, solve_lambert\n", "\n", "print(\"Imports successful.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Demonstration: Clohessy-Wiltshire Propagation\n", "\n", "We simulate a chaser starting 1 km behind and 500m above the target with some relative velocity offset." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_orbit = 0.0011 # Mean motion (rad/s) for a standard LEO orbit\n", "r0 = np.array([0.5, -1.0, 0.0]) # [x, y, z] in km (500m radial node higher, 1km behind)\n", "v0 = np.array([0.0, 0.0, 0.0]) # stationary relative to target initially\n", "\n", "time = np.linspace(0, 3600, 100) # 1 hour simulation\n", "history_r = []\n", "\n", "for t in time:\n", " r_t, v_t = cw_equations(r0, v0, n_orbit, t)\n", " history_r.append(r_t)\n", " \n", "history_r = np.array(history_r)\n", "\n", "plt.figure(figsize=(10, 6))\n", "plt.plot(history_r[:, 1], history_r[:, 0], 'b-', label='Chaser Trajectory')\n", "plt.plot(0, 0, 'ro', label='Target')\n", "plt.xlabel('Along-track (Y) [km]')\n", "plt.ylabel('Radial (X) [km]')\n", "plt.title('Relative Motion in LVLH Frame (CW Propagation)')\n", "plt.gca().invert_xaxis() # Target is ahead on negative Y for chaser scaling commonly\n", "plt.legend()\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. CW Targeting (Rendezvous)\n", "\n", "Now we calculate an impulse to rendezvous with the target ($r_{target} = [0, 0, 0]$) in 30 minutes." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial Relative Position: [ 0.5 -1. 0. ] km\n", "Required Burn Velocity v0: [-0.00111513 -0.00065579 0. ] km/s\n", "Delta-V Needed: 0.001294 km/s\n", "\n", "Position at t=1800.0s: [2.22044605e-16 0.00000000e+00 0.00000000e+00] km (Should be near [0,0,0])\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_transfer = 1800.0 # 30 minutes\n", "r_target = np.array([0.0, 0.0, 0.0]) # Meet the target\n", "\n", "v0_req = cw_targeting(r0, r_target, t_transfer, n_orbit)\n", "\n", "print(f\"Initial Relative Position: {r0} km\")\n", "print(f\"Required Burn Velocity v0: {v0_req} km/s\")\n", "print(f\"Delta-V Needed: {np.linalg.norm(v0_req):.6f} km/s\")\n", "\n", "# Verify by propagating with required v0\n", "r_final, v_final = cw_equations(r0, v0_req, n_orbit, t_transfer)\n", "print(f\"\\nPosition at t={t_transfer}s: {r_final} km (Should be near [0,0,0])\")\n", "\n", "# --- Visualization of Targeted Rendezvous ---\n", "time_targeting = np.linspace(0, t_transfer, 100)\n", "history_r_target = []\n", "\n", "for t in time_targeting:\n", " r_t, v_t = cw_equations(r0, v0_req, n_orbit, t)\n", " history_r_target.append(r_t)\n", " \n", "history_r_target = np.array(history_r_target)\n", "\n", "plt.figure(figsize=(10, 6))\n", "plt.plot(history_r_target[:, 1], history_r_target[:, 0], 'g-', label='Chaser Trajectory (Targeted)')\n", "plt.plot(0, 0, 'ro', label='Target')\n", "plt.xlabel('Along-track (Y) [km]')\n", "plt.ylabel('Radial (X) [km]')\n", "plt.title('Relative Motion supporting CW Targeting')\n", "plt.gca().invert_xaxis()\n", "plt.legend()\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Lambert Solver Targeting\n", "\n", "For large absolute separations or higher accuracy, we solve the boundary value problem." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- Lambert Solver State ---\n", "Required v1 at r1: [1.41321741 6.87245562 0. ] km/s\n", "Required v2 at r2: [-6.87245562 -1.41321741 -0. ] km/s\n", "Energy-like requirement: 7.0163 km/s v1 depth\n" ] } ], "source": [ "mu = 398600.4418\n", "r1_eci = np.array([7000.0, 0.0, 0.0]) # 7000 km radius\n", "r2_eci = np.array([0.0, 7000.0, 0.0]) # 90-degree phasing\n", "dt_lambert = 1800.0 # 1800 seconds\n", "\n", "v1_req, v2_req = solve_lambert(r1_eci, r2_eci, dt_lambert, mu)\n", "\n", "print(\"--- Lambert Solver State ---\")\n", "print(f\"Required v1 at r1: {v1_req} km/s\")\n", "print(f\"Required v2 at r2: {v2_req} km/s\")\n", "print(f\"Energy-like requirement: {np.linalg.norm(v1_req):.4f} km/s v1 depth\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 4 }